Statistical Evidence Reveals How Success Breeds Success In Sport

August 8, 2012

Statistical Evidence Reveals How Success Breeds Success In Sport

In the 1980s, psychologists showed that the hot hand idea in basketball was based on the misperception of random sequences. Now a statistical study of cricket scores suggests that it may have been premature to abandon the idea that success breeds success in sport

The ‘hot hand’ idea in sport is the belief that players who have had success in the past are more likely to be successful in the future.

The most famous example is in basketball where many fans believe that a player is more likely to make a shot if he or she has successfully made the last 2 or 3 shots. In other words, the player has a ‘hot hand’.

Back in the 1980s, three cognitive psychologists decided to take a closer look at this idea. Their studies showed that basketball fans indeed believed in the hot hand idea in shot sequences. They then examined the actual shot success rate of specific players to see if there was any truth in the idea.

The results were a surprise, at least for basketball fans. While some players are certainly better shooters than other players, the psychologists found no evidence of a hot hand phenomenon. The chances of success on the next shot are not correlated with the success of the last shot. In other words the hot hand idea is a fallacy.

The psychologists attributed the effect to a general misunderstanding of random sequences: long sequences of successful (and unsuccessful) shots naturally occur at random. They just look as if the player has a hot hand.

(A similar effect occurs in coin tossing experiments when people think a tail is more likely to occur after a long sequence of heads. This is known as the gambler’s fallacy.)

In 1985, they published their results in a paper called “The Hot Hand in Basketball: On the Misperception of Random Sequences” and since then hot hand effect has been generally considered a fallacy.

But as a sports fan, it’s hard to let go of the idea that success breeds success. Indeed, there has been huge debate since then over whether hot hand effects exist or not.

Today, researchers reveal that the hot hand effect is alive and well in the game of cricket.

The evidence comes from the work of Haroldo Ribeiro at the Universidade Estadual de Maringa in that well known cricket-loving country, Brazil, and a couple of pals.

These guys have examined the rate of scoring in three types of international cricket match played between 2002 and 2011. The three types are T20, which lasts for about 3 hours, one day games which last for about 8 hours and Test cricket, which lasts for five days.

The hot hand phenomenon is a type of memory effect since future performance is determined by events in the past. Because of this, there are well-established statistical techniques for revealing its presence.

Ribeiro and co duly put the data through its paces, examining not only the evolution of the scores over time but their variance too. They say they can clearly see long range memory effects at work. “This result shows that there is long-range memory in the score evolution… positive values are followed by positive values and negative values are followed by negative values much more frequently than by chance,” they say.

So if a cricket team starts off scoring well it is more likely to score strongly later in its innings. Conversely, if a team starts badly, it is more likely to continue this poor run.

Interestingly, this effect is just as clear in Test cricket over 5 days as it is in T20 cricket over three hours. So the memory effect works over extremely long timescales, compared for example to basketball shooting sequences.

“The long-range persistent behavior in the score evolution not only indicates the existence of this phenomenon in cricket, but also suggests that this phenomenon can act over a very long temporal scale,” say Ribeiro and co.

That’s an interesting result. Cricket is a hugely psychological game in which confidence plays a major role. If confidence is contagious, it makes sense that early success can lead to success in the future.

Ribeiro and co say their methods can be applied to other sports as well so it should be possible to see the statistical fingerprint of a hot hand effect in other areas too.

The next question is whether this will effect sports strategy in future and in what way. Suggestions in the comments section below.

Ref: arxiv.org/abs/1208.1204: Anomalous Diﬀusion and Long-range Correlations in the Score Evolution of the Game of Cricket